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Oct
9
comment Partial derivative help
@ben: Yes, that's what I meant. For instance, in your second displayed equation, it's not clear where $\partial f/\partial x$ is to be evaluated, since $x$ (which would be the default assumption if the argument isn't specified) doesn't occur as a variable in that equation. Yes, you have two ways of showing appreciation. One is to accept one of the answers by clicking on the checkmark to the left of it under the vote tally, but you can only do that for one answer; the other is to upvote it with the up-arrow above the vote tally; you need $15$ points yourself to do that (which you have).
Oct
9
comment Derivation of Goldstein's rotation formula
Note that $|\mathbf u-\langle\mathbf u,\mathbf n\rangle\mathbf n|=|\mathbf u\times\mathbf n|=NU=NV$, so all those factors actually cancel (leading to the result in the first displayed equation in the question). See also the Wikipedia article (which doesn't mention "Goldstein's rotation formula" as an alternative name; is that how the book calls it?).
Oct
9
revised Partial derivative help
more direct evaluation
Oct
9
answered Partial derivative help
Oct
9
comment Partial derivative help
If $x=x(y)$ and $f=f(x)$, why are you writing their derivatives as partial derivatives?
Oct
9
revised Does this matrix have a name?
edited tags
Oct
9
revised proving a certain split is impossible
typo
Oct
9
answered proving a certain split is impossible
Oct
9
comment Formula that takes on all integers
There have been two further downvotes. Could the downvoters please explain their downvotes? Please see the FAQ: "If you see misinformation, vote it down. Add comments indicating what, specifically, is wrong." Also, please note that this is an answer to a previous version of the question, as explained in my comment under the question. You can see the previous versions of the question by clicking on the link "edited ..." underneath the question.
Oct
9
comment Pseudo Inverse Solution for Linear Equation System Using the SVD
@user1551: Thanks :-)
Oct
9
comment Spanning trees in a ladder graph
@Alex: I've added an alternative solution of the recurrence to my answer.
Oct
9
revised Spanning trees in a ladder graph
added solution with matrix diagonalization
Oct
8
answered Given a random graph $G_{n,p}$, how to get the expectation of number of components with $k$ vertices and $k$ edges?
Oct
8
answered Systems of polynomial equations
Oct
8
revised transforming vector potential with a coordinate rotation
formatting
Oct
8
comment Deleting any digit yields a prime… is there a name for this?
That's not surprising if you look at my estimates. Solutions with few digits are rare; most of the solutions have around $10$ strings of repeated digits.
Oct
8
revised Reference: Representation Theory
spelling
Oct
8
comment Deleting any digit yields a prime… is there a name for this?
Note that my estimate predicts $0.64$ solutions with repeated last digit with $332$ digits even if the original number is prime. Dropping the condition that the original number is prime removes a factor $p_m$ and increases the expected number of solutions to $489$. For most of these the number of strings of repeated digits is around the average value of $10$; the expected number of solutions with $332$ digits, repeated last digit and only $2$ strings of repeated digits is about $0.32$.
Oct
8
comment Tile $\mathbb{R}^n$ with Primitive Cuboids
@t.b.: I see, thanks, sorry.
Oct
8
comment Is there a clever solution to this elementary probability/combinatorics problem?
+1 -- very nice :-) This also immediately yields the generalized version that the probability for $k$ balls is $2/(k+1)$.